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Concurrent Realizability on Conjunctive Structures Beffara, Emmanuel Castro, Félix Guillermo, Mauricio Miquey, Étienne Realizability Process Algebras Concurrent Processes Linear Logic This work aims at exploring the algebraic structure of concurrent processes and their behavior independently of a particular formalism used to define them. We propose a new algebraic structure called conjunctive involutive monoidal algebra (CIMA) as a basis for an algebraic presentation of concurrent realizability, following ideas of the algebrization program already developed in the realm of classical and intuitionistic realizability. In particular, we show how any CIMA provides a sound interpretation of multiplicative linear logic. This new structure involves, in addition to the tensor and the orthogonal map, a parallel composition. We define a reference model of this structure as induced by a standard process calculus and we use this model to prove that parallel composition cannot be defined from the conjunctive structure alone. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Emmanuel Beffara and Félix Castro and Mauricio Guillermo and Étienne Miquey 2023 Is Part Of LIPIcs, Volume 260, 8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.FSCD.2023.28 urn:nbn:de:0030-drops-180124 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2023.28 eng https://creativecommons.org/licenses/by/4.0/legalcode